Friday, 25 April 2014

"Teach Me ANYTHING in 5 Minutes" They Said:

Reflections on a (Successful) Interview or How I learned to Stop Worrying and Embrace Mayo as a Metaphor for Math

I just found out that beyond having to catch up on the #MTBoS Missions from the fall there is also now currently a 30 days of blogging challenge under the #MTBoS30 tag. Not sure I'll do an everyday blog, but that's no reason not to post now (the dishes and the 30 minutes window before I start my evening restaurant shift are, but that hopefully will excuse some of the license I'm bound to take with things like spelling, grammar, punctuation....

I interviewed today for a second tutoring job. I love the place I tutor at currently, it's a centre with cats, dogs, tea and snacks, many textbooks, laptops, etc. I get emails with my appointments/cancellations, go there a bit before the appointed time and get to tutor high school preCalc, Calc, and first year Calc, plus some other stuff when it comes up.

I applied for this new place because I saw an add posted online for a tutor for an elementary school student in my neighbourhood for in home tutoring. I've done this before, prior to my B.Ed program and am looking forward to how I will have changed as a tutor since then. I'm also looking at more elementary level education right now, whereas the last year or so has been more high school level. [I'm into doing it all, but have to pick jobs to apply for and the AQ/PD courses to take.]

I had a skype interview that went well and I was asked to come in this morning to do a group session with a few other tutoring candidates (we were not in direct competition; I think it was to see how we engaged with other people and to save time overall). We were all asked to be prepared to teach the interviewer ANYTHING in about a 5 minute time frame, assuming no prior knowledge. 

I thought about doing the division algorithm I prefer (see previous post) or radian measures or doing some sort of lesson on math stuff. I find direct instruction kind of boring and the interviewer had said we could teach her ANYTHING and mentioned that someone had done magic, someone else had done a game; things like that. I got stuck on the idea of cooking something, in particular of making mayo. 

I have worked in restaurants for about 10 years now (on and off, mostly on, but with some time off during my undergrad and B.Ed programs; plus that year of farming that is food related but not restaurant work directly....). I worked at a French Bistro in Guelph that made handmade mayo and salad dressing exclusively. That worked out to 4-6L of each, up to 3 times a week. And by hand, I mean with a big whisk and a large bowl and me (or whomever) feeling like their arm was going to fall off. Every once and a while a new chef would use the blender and no one could tell the difference ... but the chef wanted it done by hand.

Mayo is an emulsion (read: mixture) of oil and water, which don't normally like to be mixed. You can see this if you dump some oil into a glass or bowl of water. It's bound with a raw egg yolk, flavoured with vinegar and (often) mustard, salt and pepper. The only trick is to whisk REALLY hard at the start so the emulsion starts to form while adding in the oil VERY, VERY slowly. 

I think it took a bit more than 5 minutes, maybe even closer to 10. Especially considering I got the interviewer to go wash her hands (good food prep practice) while I set up the supplies on the table and poured oil into a couple 1 Cup mugs I had brought along. I had the interviewer follow along with me as we both made mayo in separate bowls. 

It got me thinking about math and cooking. How both have standard and important algorithms and practices (I actually refer to a lot of math "bits" as recipes when talking to students and think connects a bit more to their worlds). Learning one thing in both often helps learn other things. The emulsion we did is useful not just for making mayo, but also for salad dressing and sauces like hollandaise. 

In both cases though, knowing the algorithms is really far off from doing the thing. Answering a real problem with math (and mathematical thinking) and making dinner for yourself or your family are much more than factoring a quadratic or making a basic emulsion, but the more of the underlying stuff you know the easier it is for you to put it together in a way that makes sense to the context your in (and that you find pleasing to eat.) In both cases you need the confidence to think that you can do the whole thing, and that you can find your way to a solution, even if something goes off the rails somewhere along the way. 

My worlds are colliding! Now off to work. 

Wednesday, 23 April 2014

Late to the Party

Exploring the #MTBOS Mission #1: An Introduction

Hi! I'm Matt Leiss. I'm a newly certified teacher in Toronto, Ontario. I did my undergrad in Math at McMaster University and after a few years found myself in Ottawa where I completed my B.Ed degree. I had a great experience at teacher's college and almost two years after graduating I am still excited and passionate about teaching in general and math education in particular. I'm trying out as many roles, jobs, grade levels and entry points to this career as I can. I'll try to keep my happenings posted on twitter (@mrleiss)!

I want to write about what drew me into the #MTBoS and a bit about my relationship with technology. So here it goes!

About a year ago I took a position with an online High School startup company to develop a course in line with the Ontario curriculum. My math background is/was definitely strong enough even though I took the Junior/Intermediate stream during my B.Ed (I specialized in Pure Math during my undergrad) and I had done some basic website design in high school so I knew a bit of html and knew I could find tutorials to walk me through other stuff as it came up. I didn't (and still don't) have a lot of experience creating web content, filming videos, editing photos, etc. My main experience with Learning Management Systems (LTS) was with how badly they were used during my undergrad to store course outlines and host unmoderated discussion forums.

I had just been given an iPod Touch as a gift from my wife (I had been talking about getting one for about two years). I should note I only ever had a cell phone for about 6 months, way way before they were SMART. I have tended to take to new technology slowly, begrudgingly while rambling things about being a luddite at heart.... So I took to the podcasts, the googles, the web and eventually to the twitters. It was very slow at first. I think I added the promotional accounts for the online school, the principal, and some of the other staff and that was about it.

My big break came when I found the podcast "On Online Education" by Eric Wignall. I listened to the episodes on the subway to and from the tutoring centre I work at and have continued to listen to them even after I stepped back from creating content for the school. (I haven't been able to find anything by him recently but if you know of other work of his or twitter contacts please post it in the comments). One episode really rocked my work. It was an interview with Maria Anderson (@busynessgirl). I have probably listened to it a half dozen times now.

Somehow through Maria I found David Wees (@davidwees) a fellow Canadian, whose last name I assume is pronounced similar to mine (although I could be way off too!). Through these two fine folks I found some of the other rock stars of the #mtbos. Too many of you to mention; not enough of you I have dropped into my digg reader account or have been able to follow your blogs. I keep wondering if there is a way to just add all the blogs from someone else's list and then either remove or edit that as I go. Perhaps it's better to have to add blogs a few at a time so I get a better grip for what's there. I don't know?! I'm still learning how to do this internet thing!

The Explore the Math Twitter Blog-o-Sphere Missions (here) came up while I was swamped working a contract at a private international school to teach high school math (and eventually accounting) to Mandarin speaking students from China. I wanted to take part in the challenges at the time, and I think I half did a couple of them, but I did gain a lot from lurking the posts and seeing the half conversations with other great math teachers on twitter. Just like blogs, I'm still learning and use basic twitter on my iPod to browse posts, get notifications, and favourite things I want to read later. I have tweet deck with lots of columns on my computer and am always hoping to check there more often and take part more. I added a few lists from others to my general feed and am not sure that was the best approach for me. I'm sure I'm going to go back and forth between keeping a limited scope feed and a big net approach of trying to get it all in.

The Missions gave me the chance to find a LOT more of you, to learn about the math chats (need to get more into them...), the global math department, so many things. I also got to start to learn about you as people. Listening to Infinite Tangents by Ashli (@mythagon) and reading Justin Aion's blog (here) have really helped me to get to know the community as a place to come for support on bad days and to feel connected to what is going on in education on a wider scale then I would know without it.

Just like the iPod Touch, I've been talking and thinking about getting a tablet for a while now mainly because I want to read more online (mainly your blogs, but also for the AQ and PD courses I need to start taking soon) and so I can blog more on the go. My laptop battery has been fried since one of the cats chewed the cable one too many times so it's a plug in only machine. I'm hoping to go through all the challenges this spring (unless other opportunities get in the way) and blog more. Having a place to put my reflections and ideas is going to be good for me.

My last thought for this post is that I use linux on my laptop. I think I like the challenge of having to learn how to do things, even though it can be really frustrating too. Currently I'm running Xubuntu 12.04 LTS and am having a few funny glitches, but nothing major. Geogebra and Desmos run well on it (two of the math technologies I am in shear awe of and only found because of the #mtbos) and my Dropbox and Google accounts/files seem to be fine opening in linux day, on my iPod the next, and on the windows machines I have access to at jobs. 

Friday, 18 April 2014

How I'd like to teach Division

(Not Your Parent's) Long Division:

Dividing requires finding out how many "times" a number "goes into"another. It's really just counting and subtracting

Divide 2467 by 14

Start by taking one 14 out of 2467.

2467 - 14 = 2453

And then another,

2453 - 14 = 2439 

and another!

2439 - 14 = 2425

14 has been removed 3 times. The division question, really, is asking if this pattern were continued until no more 14's could be taken out, how many 14's would have been removed in total.

Speed up by taking out ten 14's at once.

 2439 - (14 X 10) = 2439 - 140 = 2285 

Or 100!
2285 - (14 X 100) = 2299 - 1400 = 885

14 has now been removed 113 times! Completing the remaining steps could look like this.

885- (10 X 14) = 855 - 140 = 745

745 - (10 X 14) = 745 - 140 = 605

605 - (10 X 14) = 605 - 140 = 465

465 - (10 X 14) = 465 - 140 = 325

325 - (10 X 14) = 325 - 140 = 185

185 - (10 X 14) = 185 - 140 = 45

45 - 14 = 31

31 - 14 = 17

17 - 14 = 3

Counting the total number of 14's removed: 3 + 10 + 100 + 60 + 3 = 176.

That number leftover, in this case 3, is called The Remainder


Once students grasp the general mechanics of dividing numbers and can see division as a method to split into pieces, group items, etc. They are made to divide larger and larger dividend by larger and larger divisors. Ultimately students (and everyone else) reach for calculators, which is all well and good, but what about when you don't have access to a calculator (rare these days, save for the constraints of very restrictive test environments). Long division is the answer according to math teachers for the last .... years (I don't know when this algorithm came about; I'm curious). 

We shouldn't go as far as to say Long Division is bunk or useless. It's not. It is a pretty necessary algorithm used in high school division of polynomials. BUT it is overly restrictive about format and removes the choice students can make about what multiple of the divisor they want to remove at each step. Student with stronger multiplication skills may take fewer steps, but I don't see any real benefit in a student knowing that 140 goes into 1067 exactly 7 times (which is what Long Division would require here after dividing 2467 by 1 X 14 X 100).

Long Division is a special case of this division procedure. I'm not sure which would be easier to write up a pure algorithm for or describe to a computer. Which is the kind of question I plan to put to my students in regards to algorithms and the kind of thinking I want them to develop alongside, the why does it work and when might it not work.

I think generally it's a lot easier to remove the larger multiples first. Perhaps partly because we have more experience and therefore comfort with smaller numbers. I wonder if starting with removing a single number would slow students down in terms of seeing this.

I think that I would plan to leave it to students to realize for themselves that they can remove multiples that are not powers of 10. I think 2 and 5 are good ones for lots of division problems.

Oh, a game that will lead to the more traditional long division is to challenge students to the same numbers in the fewest possible steps.

Not sure of the easiest or cleanest way to set this up on a page. The important part is that students can easily count the number of divisors removed and have space to compute the subtraction when necessary.